Moduli spaces of gauge theories in 3 dimensions.

The objective of this thesis is to study the moduli spaces of pairs of mirror theories in 3 dimensions with N = 4. The original conjecture of 3d mirror symmetry was motivated by the fact that in these pairs of theories the Higgs and Coulomb branches are swapped. After a brief introduction to supersymmetry we will first focus on the Higgs branch. This will be investigated through the Hilbert series and the plethystic program. The methods used for the Higgs branch are very well known in literature, more difficult is the case of the Coulomb branch since it receives quantum corrections. We will explain how it is parametrized in term of monopole operators and having both Higgs and Coulomb branches for theories with different gauge groups we will be able to show how mirror symmetry works in the case of ADE theories. We will show in which cases these Yang- Mills vacua are equivalent to one instanton moduli spaces.ope

Online Learning, Physics and Algorithms

In recent years, we have witnessed an increasing cross-fertilization between the fields of computer science, statistics, optimization and the statistical physics of learning. The area of machine learning is at the interface of these subjects. We start with an analysis in the statistical physics of learning, where we analyze some properties of the loss landscape of simple models of neural networks using the computer science formalism of Constraint Satisfaction Problems. Some of the techniques we employ are probabilistic, but others have their root in the studies of disorder systems in the statistical physics literature. After that, we focus mainly on online prediction problems, which were initially investigated in statistics but are now very active areas of research also in computer science and optimization, where they are studied in the adversarial case through the lens of (online) convex optimization. We are particularly interested in the cooperative setting, where we show that cooperation improves learning. More specifically, we give efficient algorithms and unify previous works under a simplified and more general framework

Cooperative Online Learning

In this preliminary (and unpolished) version of the paper, we study an asynchronous online learning setting with a network of agents. At each time step, some of the agents are activated, requested to make a prediction, and pay the corresponding loss. Some feedback is then revealed to these agents and is later propagated through the network. We consider the case of full, bandit, and semi-bandit feedback. In particular, we construct a reduction to delayed single-agent learning that applies to both the full and the bandit feedback case and allows to obtain regret guarantees for both settings. We complement these results with a near-matching lower bound

Clustering of solutions in the symmetric binary perceptron

The geometrical features of the (non-convex) loss landscape of neural network models are crucial in ensuring successful optimization and, most importantly, the capability to generalize well. While minimizers' flatness consistently correlates with good generalization, there has been little rigorous work in exploring the condition of existence of such minimizers, even in toy models. Here we consider a simple neural network model, the symmetric perceptron, with binary weights. Phrasing the learning problem as a constraint satisfaction problem, the analogous of a flat minimizer becomes a large and dense cluster of solutions, while the narrowest minimizers are isolated solutions. We perform the first steps toward the rigorous proof of the existence of a dense cluster in certain regimes of the parameters, by computing the first and second moment upper bounds for the existence of pairs of arbitrarily close solutions. Moreover, we present a non rigorous derivation of the same bounds for sets of $y$ solutions at fixed pairwise distances

An explainable model of host genetic interactions linked to COVID-19 severity

We employed a multifaceted computational strategy to identify the genetic factors contributing to increased risk of severe COVID-19 infection from a Whole Exome Sequencing (WES) dataset of a cohort of 2000 Italian patients. We coupled a stratified k-fold screening, to rank variants more associated with severity, with the training of multiple supervised classifiers, to predict severity based on screened features. Feature importance analysis from tree-based models allowed us to identify 16 variants with the highest support which, together with age and gender covariates, were found to be most predictive of COVID-19 severity. When tested on a follow-up cohort, our ensemble of models predicted severity with high accuracy (ACC = 81.88%; AUCROC = 96%; MCC = 61.55%). Our model recapitulated a vast literature of emerging molecular mechanisms and genetic factors linked to COVID-19 response and extends previous landmark Genome-Wide Association Studies (GWAS). It revealed a network of interplaying genetic signatures converging on established immune system and inflammatory processes linked to viral infection response. It also identified additional processes cross-talking with immune pathways, such as GPCR signaling, which might offer additional opportunities for therapeutic intervention and patient stratification. Publicly available PheWAS datasets revealed that several variants were significantly associated with phenotypic traits such as "Respiratory or thoracic disease", supporting their link with COVID-19 severity outcome.A multifaceted computational strategy identifies 16 genetic variants contributing to increased risk of severe COVID-19 infection from a Whole Exome Sequencing dataset of a cohort of Italian patients

Carriers of ADAMTS13 Rare Variants Are at High Risk of Life-Threatening COVID-19

Thrombosis of small and large vessels is reported as a key player in COVID-19 severity. However, host genetic determinants of this susceptibility are still unclear. Congenital Thrombotic Thrombocytopenic Purpura is a severe autosomal recessive disorder characterized by uncleaved ultra-large vWF and thrombotic microangiopathy, frequently triggered by infections. Carriers are reported to be asymptomatic. Exome analysis of about 3000 SARS-CoV-2 infected subjects of different severities, belonging to the GEN-COVID cohort, revealed the specific role of vWF cleaving enzyme ADAMTS13 (A disintegrin-like and metalloprotease with thrombospondin type 1 motif, 13). We report here that ultra-rare variants in a heterozygous state lead to a rare form of COVID-19 characterized by hyper-inflammation signs, which segregates in families as an autosomal dominant disorder conditioned by SARS-CoV-2 infection, sex, and age. This has clinical relevance due to the availability of drugs such as Caplacizumab, which inhibits vWF-platelet interaction, and Crizanlizumab, which, by inhibiting P-selectin binding to its ligands, prevents leukocyte recruitment and platelet aggregation at the site of vascular damage